Sets Test

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Sets Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

A set has 7 elements. The number of elements in its power set is:

A
32

B
24

C
64

D
128

Solution

If n(A) = m , then number of elements in its power set = 2^m

Hence, number of elements in power set of A = 2⁷ = 128
Question 2
1 / -0

For any sets A and B, P(A∩B)=

A
P(A) x P(B)

B
P(A) υ P(B)

C
P(A)/P(B)

D
P(A)∩P(B)

Solution

An element which belongs to P(A∩B) i.e. the power set of (A∩B) has to be a subset of A and B both. So it must belong to P(A) as well as P(B). Similarly an element which belongs to P(A)∩P(B) must belong to P(A) as well as P(B) and hence to A and B both. Thus, it must be in P(A∩B).
Question 3
1 / -0

In a certain class 15 students play basket-ball, 13 play chess and 5 play both the games. How many students are there in the class assuming that each students play at least one of the game?

A
23

B
43

C
33

D
48

Solution

n (P) : Number of students who play basket ball = 15

n (Q) : Number of students who play chess = 13

n (P^∩Q): Number of students who play both the games = 5 14

n(PUQ) = n (P) + n(Q) - n (P^∩Q)

= 15 + 13 -5 = 23
Question 4
1 / -0

How many elements does P(A) have, If A = Φ

A
4

B
0

C
1

D
2

Solution

Here A = Φ i.e. n(A) = 0 , therefore n [P(A)] = 2⁰ = 1
Question 5
1 / -0

If U, the universal set, is the set of all students of a school which are in classes from I to X and B = set of all students of class X. What is B'?

A
set of all students of class I to VIII

B
set of all students of class VIII

C
set of all students of class IX

D
set of all students from classes I to IX

Solution

U = set of all students from classes I to IX

The complement of a subset B of universal set U is the set of all elements of U which are not the elements of B .

Hence B' = set of all students from classes I to IX
Question 6
1 / -0

Given the sets P = {2,4,6}, Q = {3,5,7} and R = {1,3,5,7,9}, which of the following may be considered as universal set for all the three sets P, Q and R?

A
Φ

B
{2,3,4,5,6,7}

C
{1,3,5,7,9}

D
{1,2,3,4,5,6,7,9}

Solution

The universal set is a super set of all given sets under consideration. Hence, {1,2,3,4,5,6,7,9} is universal set for P, Q and R as it contains all the elements in P, Q and R.
Question 7
1 / -0

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set for all the three sets A, B and C?

A
{0, 1, 2, 3, 4, 5, 6, 8}

B
Φ

C
{0,1,2,3,4,5,6,7,9,10}

D
{1,2,3,4,5,6,7,8}

Solution

Universal set contains every element that is relevant to the sets under consideration.

So the universal set here is {0,1,2,3,4,5,6,8}
Question 8
1 / -0

The set builder form of the set B = {2, 3, 5, 7, 11} is

A
B = {x : x is an odd natural number less than 12}

B
B = {x : x is a prime number less than 12}

C
B = {x : x is a cube of a natural number less than 12}

D
B = {x : x is an odd natural number less than 11}

Solution

2 is the smallest prime number. All the other numbers are also prime less than 12.

Hence, option B is correct.

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Re-Attempt Weekly Quiz Competition

Sets Test - 3

Result

Sets Test - 3

Score

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Rank

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SHARING IS CARING

Question 1

32

24

64

128

Solution

Question 2

P(A) x P(B)

P(A) υ P(B)

P(A)/P(B)

P(A)∩P(B)

Solution

Question 3

23

43

33

48

Solution

Question 4

4

0

1

2

Solution

Question 5

set of all students of class I to VIII

set of all students of class VIII

set of all students of class IX

set of all students from classes I to IX

Solution

Question 6

Φ

{2,3,4,5,6,7}

{1,3,5,7,9}

{1,2,3,4,5,6,7,9}

Solution

Question 7

{0, 1, 2, 3, 4, 5, 6, 8}

Φ

{0,1,2,3,4,5,6,7,9,10}

{1,2,3,4,5,6,7,8}

Solution

Question 8

B = {x : x is an odd natural number less than 12}

B = {x : x is a prime number less than 12}

B = {x : x is a cube of a natural number less than 12}

B = {x : x is an odd natural number less than 11}

Solution

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